Question

If sin(a+2b)=√3/2 andcos(a+4b)=0,0

Answer 1

$\sin( \alpha + 2 \beta ) = \frac{ \sqrt{3} }{2} \\ \\ \boxed{\alpha + {2 \beta = \frac{\pi}{3}}} \: \: \: - - eq.(1) \\ \\ \cos( \alpha + 4 \beta ) = 0 \\ \\ \boxed{ \alpha + 4 \beta = \frac{\pi}{2} } \: \: \: - - eq.(2) \\ \\ Solving \: \: eq.(1) \: \: and \: \: eq.(2) \: \: , \: \\ \\ \large \boxed{\alpha = \frac{\pi}{6} \: \: \: \: \: \: \: \: \beta = \frac{\pi}{12} }$